Improving morphological and functional properties of enteric neuronal networks in vitro using a novel upside-down culture approach.

The enteric nervous system (ENS) comprises millions of neurons and glia embedded in the wall of the gastrointestinal tract. It not only controls important functions of the gut but also interacts with the immune system, gut microbiota, and the gut-brain axis, thereby playing a key role in the health and disease of the whole organism. Any disturbance of this intricate system is mirrored in an alteration of electrical functionality, making electrophysiological methods important tools for investigating ENS-related disorders. Microelectrode arrays (MEAs) provide an appropriate noninvasive approach to recording signals from multiple neurons or whole networks simultaneously. However, studying isolated cells of the ENS can be challenging, considering the limited time that these cells can be kept vital in vitro. Therefore, we developed an alternative approach cultivating cells on glass samples with spacers (fabricated by photolithography methods). The spacers allow the cells to grow upside down in a spatially confined environment while enabling acute consecutive recordings of multiple ENS cultures on the same MEA. Upside-down culture also shows beneficial effects on the growth and behavior of enteric neural cultures. The number of dead cells was significantly decreased, and neural networks showed a higher resemblance to the myenteric plexus ex vivo while producing more stable signals than cultures grown in the conventional way. Overall, our results indicate that the upside-down approach not only allows to investigate the impact of neurological diseases in vitro but could also offer insights into the growth and development of the ENS under conditions much closer to the in vivo environment.NEW & NOTEWORTHY In this study, we devised a novel approach for culturing and electrophysiological recording of the enteric nervous system using custom-made glass substrates with spacers. This allows to turn cultures of isolated myenteric plexus upside down, enhancing the use of the microelectrode array technique by allowing recording of multiple cultures consecutively using only one chip. In addition, upside-down culture led to significant improvements in the culture conditions, resulting in a more in vivo-like growth.

3D Fractal Dimension Analysis: Prognostic Value of Right Ventricular Trabecular Complexity in Participants with Arrhythmogenic Cardiomyopathy.

BACKGROUND: Arrhythmogenic cardiomyopathy (ACM) is characterized by progressive myocardial fibro-fatty infiltration accompanied by trabecular disarray. Traditionally, two-dimensional (2D) instead of 3D fractal dimension (FD) analysis has been used to evaluate trabecular disarray. However, the prognostic value of trabecular disorder assessed by 3D FD measurement remains unclear. PURPOSE: To investigate the prognostic value of right ventricular trabecular complexity in ACM patients using 3D FD analysis based on cardiac MR cine images. STUDY TYPE: Retrospective. POPULATION: 85 ACM patients (mean age: 45 ± 17 years, 52 male). FIELD STRENGTH/SEQUENCE: 3.0T/cine imaging, T2-short tau inversion recovery (T2-STIR), and late gadolinium enhancement (LGE). ASSESSMENT: Using cine images, RV (right ventricular) volumetric and functional parameters were obtained. RV trabecular complexity was measured with 3D fractal analysis by box-counting method to calculate 3D-FD. Cox and logistic regression models were established to evaluate the prognostic value of 3D-FD for major adverse cardiac events (MACE). STATISTICAL TESTS: Cox regression and logistic regression to explore the prognostic value of 3D-FD. C-index, time-dependent receiver operating characteristic (ROC) curves and area under the ROC curve (AUC) to evaluate the incremental value of 3D-FD. Intraclass correlation coefficient for interobserver variability. P < 0.05 indicated statistical significance. RESULTS: 26 MACE were recorded during the 60 month follow-up (interquartile range: 48-67 months). RV 3D-FD significantly differed between ACM patients with MACE (2.67, interquartile range: 2.51 ~ 2.81) and without (2.52, interquartile range: 2.40 ~ 2.67) and was a significant independent risk factor for MACE (hazard ratio, 1.02; 95% confidence interval: 1.01, 1.04). In addition, prognostic model fitness was significantly improved after adding 3D-FD to RV global longitudinal strain, LV involvement, and 5-year risk score separately. DATA CONCLUSION: The myocardial trabecular complexity assessed through 3D FD analysis was found associated with MACE and provided incremental prognostic value beyond conventional ACM risk factors. EVIDENCE LEVEL: 4 TECHNICAL EFFICACY: Stage 1.

Fractal Analysis of Left Ventricular Trabeculae in Patients with End-Stage Renal Disease: A Random Survival Tree Analysis.

BACKGROUND: The complexity of left ventricular (LV) trabeculae is related to the prognosis of several cardiovascular diseases. PURPOSE: To evaluate the prognostic value of LV trabecular complexity in patients with end-stage renal disease (ESRD). STUDY TYPE: Prospective outcome study. POPULATION: 207 participants on maintenance dialysis, divided into development (160 patients from 2 centers) and external validation (47 patients from a third center) cohorts, and 72 healthy controls. FIELD STRENGTH: 3.0T, steady-state free precession (SSFP) and modified Look-Locker imaging sequences. ASSESSMENT: All participants had their trabecular complexity quantified by fractal analysis using cine SSFP images. Patients were followed up every 2 weeks until April 2023, or endpoint events happened. Random Forest (RF) and Cox regression models including age, diabetes, LV mass index, mean basal fractal dimension (FD), and left atrial volume index, were developed to predict major adverse cardiac events (MACE). Patients were divided into low- and high-risk groups based on scores derived from the RF model and survival compared. STATISTICAL TESTS: Receiver operating characteristic curve analysis; Kaplan-Meier survival analysis with log rank tests; Harrel's C-index to assess model performance. A P value <0.05 was considered statistically significant. RESULTS: Fifty-five patients (26.57%) experienced MACE during a median follow-up time of 21.83 months. An increased mean basal FD (≥1.324) was associated with a significantly higher risk of MACE. The RF model (C-index: 0.81) had significantly better discrimination than the Cox regression model (C-index: 0.74). Participants of the external validation dataset classified into the high-risk group had a hazard of experiencing MACE increased by 12.29 times compared to those in the low-risk group. DATA CONCLUSION: LV basal FD was an independent predictor for MACE in patients with ESRD. Reliable risk stratification models could be generated based on LV basal FD and other MRI variables using RF analysis. LEVEL OF EVIDENCE: 2 TECHNICAL EFFICACY: Stage 2.

Prognostic value of left ventricular trabeculae fractal analysis in patients with dilated cardiomyopathy.

BACKGROUND: The prognostic value of left ventricular (LV) myocardial trabecular complexity on cardiovascular magnetic resonance (CMR) in dilated cardiomyopathy (DCM) remains unknown. This study aimed to evaluate the prognostic value of LV myocardial trabecular complexity using fractal analysis in patients with DCM. METHODS: Consecutive patients with DCM who underwent CMR between March 2017 and November 2021 at two hospitals were prospectively enrolled. The primary endpoints were defined as the combination of all-cause death and heart failure hospitalization. The events of cardiac death alone were defined as the secondary endpoints.LV trabeculae complexity was quantified by measuring the fractal dimension (FD) of the endocardial border based on fractal geometry on CMR. Cox proportional hazards regression and Kaplan-Meier survival analysis were used to examine the association between variables and outcomes. The incremental prognostic value of FD was assessed in nested models. RESULTS: A total of 403 patients with DCM (49.31 ± 14.68 years, 69% male) were recruited. After a median follow-up of 43 months (interquartile range, 28-55 months), 87 and 24 patients reached the primary and secondary endpoints, respectively. Age, heart rate, New York Heart Association functional class >II, N-terminal pro-B-type natriuretic peptide, LV ejection fraction, LV end-diastolic volume index, LV end-systolic volume index, LV mass index, presence of late gadolinium enhancement, global FD, LV mean apical FD, and LV maximal apical FD were univariably associated with the outcomes (all P < 0.05). After multivariate adjustment, LV maximal apical FD remained a significant independent predictor of outcome [hazard ratio = 1.179 (1.116, 1.246), P < 0.001]. The addition of LV maximal apical FD in the nested models added incremental prognostic value to other common clinical and imaging risk factors (all <0.001; C-statistic: 0.84-0.88, P < 0.001). CONCLUSION: LV maximal apical FD was an independent predictor of the adverse clinical outcomes in patients with DCM and provided incremental prognostic value over conventional clinical and imaging risk factors.

Outcome of single-visit root canal treatment with or without MTAD: A randomized controlled clinical trial.

AIM: This study aimed to investigate 2-year changes in periapical trabecular patterns in single-rooted teeth with apical periodontitis using fractal analysis and periapical index (PAI) after root canal treatment performed with or without BioPure MTAD solution. METHODOLOGY: In this randomized clinical trial, 100 patients were selected and randomized to either the BioPure MTAD or the control groups. Initial periapical radiographs were obtained for each participant before and 2 years after root canal treatment. The region of interest in the periapical lesion around the root apex was selected from the paired periapical radiographs, and then, the fractal dimension (FD) was calculated. With regards to the classification of periapical status, PAI was labelled as "healed" (PAI ≤ 2) or "unhealed" (PAI ≥ 3). RESULTS: After 24 months, 28 patients did not comply with the follow-up and the data of 72 patients were compared. When the initial and the follow-up PAI scores were compared, the decrease was statistically significant in 33 of 37 teeth (89.2%) and 32 of 35 teeth (91.4%) in the BioPure MTAD and control group, respectively. In both groups, statistically significant increases were observed in FD values after 2 years in all patients (p < .001). No significant difference was found between the two groups amongst decreased PAI scores and increased FD values. CONCLUSIONS: Root canal treatments with or without BioPure MTAD irrigation contributed to periapical healing in single-visit root canal treatment. Two years after root canal treatment, the extent of the periapical trabecular bone radiographically increased, as the FD and PAI data revealed.

One-step formation of three-dimensional interconnected T-shaped microstructures inside composites by orthogonal bidirectional self-assembly method.

The fillers inside a polymer matrix should typically be self-assembled in both the horizontal and vertical directions to obtain 3-dimentional (3D) percolation pathways, whereby the fields of application can be expanded and the properties of organic-inorganic composite films improved. Conventional dielectrophoresis techniques can typically only drive fillers to self-assemble in only one direction. We have devised a one-step dielectrophoresis-driven approach that effectively induces fillers self-assembly along two orthogonal axes, which results in the formation of 3D interconnected T-shaped iron microstructures (3D-T CIP) inside a polymer matrix. This approach to carbonyl iron powder (CIP) embedded in a polymer matrix results in a linear structure along the thickness direction and a network structure on the top surface of the film. The fillers in the polymer were controlled to achieve orthogonal bidirectional self-assembly using an external alternating current (AC) electric field and a non-contact technique that did not lead to electrical breakdown. The process of 3D-T CIP formation was observed in real time using in situ observation methods with optical microscopy, and the quantity and quality of self-assembly were characterized using statistical and fractal analysis. The process of fillers self-assembly along the direction perpendicular to the electric field was explained by finite element analogue simulations, and the results indicated that the insulating polyethylene terephthalate (PET) film between the electrode and the CIP/prepolymer suspension was the key to the formation of the 3D-T CIP. In contrast to the traditional two-step method of fabricating sandwich-structured film, the fabricated 3D-T CIP film with 3D electrically conductive pathways can be applied as magnetic field sensor.

A one-step electric field-induced self-assembly method was developed to efficiently control the self-assembly of fillers along two orthogonal axes to form three-dimensional interconnected T-shaped microstructure assembles of carbonyl iron powder inside a polymer matrix.

Novel Use of Fractal Analysis for Quantifying Polymethylmethacrylate Distribution Patterns in Osteoporotic and Malignant Vertebral Compression Fractures Following Vertebroplasty.

Purpose: Fractal analysis is a mathematical tool which allows the evaluation of complex microstructural features within materials that cannot be expressed in traditional geometric terms. The purpose of this study is to quantify the differences in polymethylmethacrylate intravertebral cement spatial distribution patterns following vertebroplasty using fractal analysis through the examination of osteoporotic and malignant compression fractures. Methods: Frontal and lateral post-vertebroplasty radiographs were evaluated from 29 patients with osteoporotic and malignant compression fractures who underwent vertebroplasty. The individually treated vertebra were divided into osteoporotic (n = 35) and malignant groups (n = 41). Images underwent segmentation, thresholding, and binarization prior to fractal analysis. Fractal dimension and lacunarity values were derived from the region of interest in treated vertebrae using the "box-counting" and "gliding-box" techniques respectively using ImageJ. The mean values of both parameters were compared between the 2 groups. Results: The mean fractal dimension was significantly higher in the malignant vertebral compression fracture group (1.53 ± 0.08) compared to the osteoporotic group (1.34 ± 0.17; P < .001). Similarly, mean lacunarity values were significantly higher in the malignant fracture group (0.50 ± 0.09) compared to the osteoporotic group (0.37 ± 0.10; P < .001). Conclusions: Fractal dimension and lacunarity values of cement spatial distribution patterns obtained from the post-vertebroplasty radiographs can differentiate between benign osteoporotic and malignant vertebral compression fractures. This novel technique may be useful for evaluating cement spatial distribution patterns in spine augmentation procedures, although further research is warranted in this area.

Radiographic texture of the trabecular bone of the proximal phalanx in horses with metacarpophalangeal osteoarthritis.

Osteoarthritis (OA) is a prevalent condition in horses, leading to changes in trabecular bone structure and radiographic texture. Although fractal dimension (FD) and lacunarity have been applied to quantify these changes in humans, their application in horses remains nascent. This study evaluated the use of FD, bone area fraction (BA/TA), and lacunarity in quantifying trabecular bone differences in the proximal phalanx (P1) in 50 radiographic examinations of equine metacarpophalangeal joints with varying OA degrees. In the dorsopalmar view, regions of interest were defined in the trabecular bone of the proximal epiphysis, medial and lateral to the sagittal groove of P1. Lower BA/TA values were observed medially in horses with severe OA (P=0.003). No significant differences in FD and lacunarity were found across OA degrees (P>0.1). FD, BA/TA, and lacunarity were not effective in identifying radiographic texture changes in the P1 trabecular bone in horses with different metacarpophalangeal OA degrees.

Comparative examination of trabecular bone structure in healthy and diabetic patients with periodontitis using fractal analysis.

OBJECTIVES: Fractal analysis is a numerical method that indicates the structural patterns and complexity of the trabecular bone on radiographs. The aim of this cross-sectional study was to evaluate the trabecular bone structure in systemically healthy patients and diabetes mellitus patients with periodontitis using fractal analysis. METHOD AND MATERIALS: The study included 125 mandibular first molars of nonsmoker patients. The subjects were divided into five subgroups: diabetes mellitus patients with mild-moderate periodontitis, diabetes mellitus patients with advanced periodontitis, systemically healthy individuals with mild-moderate periodontitis, systemically healthy individuals with advanced periodontitis, and systemically healthy individuals with gingivitis (control group). Clinical periodontal parameters (pocket depth, bleeding on probing, clinical attachment loss, and bone loss) were recorded. Two specific sites located in the mesial-distal regions (n = 250) of the mandibular first molars were identified using periapical radiographs captured with a parallel technique. Fractal analysis values were calculated using the box-counting method. One-way analysis of variance (ANOVA), and Pearson correlation analysis were used for statistical evaluation. RESULTS: The highest fractal analysis values were observed in systemically healthy with gingivitis patients (mesial fractal analysis: 1.86 ± 0.01; distal fractal analysis: 1.85 ± 0.01). Patients with periodontitis (mesial fractal analysis: 1.78 ± 0.02; distal fractal analysis: 1.79 ± 0.01) exhibited lower fractal analysis values compared to the control group. There was no significant difference in mesial and distal fractal analysis values between all periodontitis groups. No correlation was found between age, sex, clinical attachment loss, bone loss, and fractal analysis (P > .05). CONCLUSIONS: Although fractal analysis values were lower in the periodontitis groups compared to the control group, fractal analysis did not demonstrate any periodontitis-associated changes of bone trabeculation in diabetes at any stage of periodontitis. Furthermore, there was no significant association between fractal analysis values and age, sex, clinical attachment, and bone loss.

Fractals, Pattern Recognition, Memetics, and AI: A Personal Journal in the Computational Neurosurgery.

In this chapter, the personal journey of the author in many countries, including Italy, Germany, Austria, the United Kingdom, Switzerland, the United States, Canada, and Australia, is summarized, aimed to merge different translational fields (such as neurosurgery and the clinical neurosciences in general, biomedical engineering, mathematics, computer science, and cognitive sciences) and lay the foundations of a new field defined computational neurosurgery, with fractals, pattern recognition, memetics, and artificial intelligence as the common key words of the journey.

Fractal Analysis in MATLAB: A Tutorial for Neuroscientists.

MATLAB is one of the software platforms most widely used for scientific computation. MATLAB includes a large set of functions, packages, and toolboxes that make it simple and fast to obtain complex mathematical and statistical computations for many applications. In this chapter, we review some tools available in MATLAB for performing fractal analyses on typical neuroscientific data in a practical way. We provide detailed examples of how to calculate the fractal dimension of 1D, 2D, and 3D data in MATLAB. Furthermore, we review other software packages for fractal analysis.

Determination of growth and developmental stages in hand-wrist radiographs : Can fractal analysis in combination with artificial intelligence be used?

PURPOSE: The goal of this work was to assess the classification of maturation stage using artificial intelligence (AI) classifiers. METHODS: Hand-wrist radiographs (HWRs) from 1067 individuals aged between 7 and 18 years were included. Fifteen regions of interest were selected for fractal dimension (FD) analysis. Five predictive models with different inputs were created (model 1: only FD; model 2: FD and Chapman sesamoid stage; model 3: FD, age, and sex; model 4: FD, Chapman sesamoid stage, age, and sex; model 5: Chapman sesamoid stage, age, and sex). The target diagnoses were accelerating growth velocity, very high growth velocity, and decreasing growth velocity. Four AI algorithms were applied: multilayer perceptron (MLP), support vector machine (SVM), gradient boosting machine (GBM) and C 5.0 decision tree classifier. RESULTS: All AI algorithms except for C 5.0 yielded similar overall predictive accuracies for the five models. In order from lowest to highest, the predictive accuracies of the models were as follows: model 1 < model 3 < model 2 < model 5 < model 4. The highest overall F1 score, which was used instead of accuracy especially for models with unbalanced data, was obtained for models 1, 2, and 3 based on SVM, for model 4 based on MLP, and for model 5 based on C 5.0. Adding Chapman sesamoid stage, chronologic age, and sex as additional inputs to the FD values significantly increased the F1 score. CONCLUSION: Applying FD analysis to HWRs is not sufficient to predict maturation stage in growing patients but can be considered a growth rate prediction method if combined with the Chapman sesamoid stage, age, and sex.

Computational Fractal-Based Analysis of Brain Tumor Microvascular Networks.

Brain parenchyma microvasculature is set in disarray in the presence of tumors, and malignant brain tumors are among the most vascularized neoplasms in humans. As microvessels can be easily identified in histologic specimens, quantification of microvascularity can be used alone or in combination with other histological features to increase the understanding of the dynamic behavior, diagnosis, and prognosis of brain tumors. Different brain tumors, and even subtypes of the same tumor, show specific microvascular patterns, as a kind of "microvascular fingerprint," which is particular to each histotype. Reliable morphometric parameters are required for the qualitative and quantitative characterization of the neoplastic angioarchitecture, although the lack of standardization of a technique able to quantify the microvascular patterns in an objective way has limited the "morphometric approach" in neuro-oncology.In this chapter, we focus on the importance of computational-based morphometrics, for the objective description of tumoral microvascular fingerprinting. By also introducing the concept of "angio-space," which is the tumoral space occupied by the microvessels, we here present fractal analysis as the most reliable computational tool able to offer objective parameters for the description of the microvascular networks.The spectrum of different angioarchitectural configurations can be quantified by means of Euclidean and fractal-based parameters in a multiparametric analysis, aimed to offer surrogate biomarkers of cancer. Such parameters are here described from the methodological point of view (i.e., feature extraction) as well as from the clinical perspective (i.e., relation to underlying physiology), in order to offer new computational parameters to the clinicians with the final goal of improving diagnostic and prognostic power of patients affected by brain tumors.

EVALUATION OF MANDIBULAR TRABECULAR AND CORTICAL STRUCTURE BY FRACTAL ANALYSIS IN HYPERLIPIDEMIA AND HYPERTENSION PATIENTS.

INTRODUCTION: This study aimed to evaluate the mandibular trabecular and cortical changes in patients with hyperlipidemia (HL) and/or hypertension (HT) using fractal dimension (FD) analysis, mandibular cortical width (MCW), panoramic mandibular index (PMI) and mandibular cortical index (MCI). MATERIALS AND METHODS: Panoramic radiographs of 100 patients were evaluated. FD measurement of three region of interest (ROI) including the angulus, corpus and interdental bone area were made. MCW, PMI and MCI were also measured and noted. RESULTS: Angulus, corpus and interdental FD values were significantly lower in three disease groups than the control group. Angulus, corpus, and interdental FD values were significantly lower in the HL+HT group than in the HL group and HT group. MCW value was significantly lower in the HL group, HT group, and HL+HT group than the control group. The cortical index C1 was more common in the control group while C2 was more common in the HT, HL and HL+HT group. CONCLUSION: The fact that FD was significantly lower in the HL+HT group compared to the HL and HT groups indicates the positive effect of their association on bone loss and quality. FD measurements on images obtained using a direct digital panoramic system can be used for treatment planning and follow-up of patients with HL and/or HT.

Radiologic evaluation of associated symptoms and fractal analysis of unilateral dens invaginatus cases.

OBJECTIVE: The aim of this study is to determine the age-based prevalence of dens invaginatus cases and to learn the radiologic findings. In addition, fractal analysis of the periapical regions of unilateral dens invaginatus cases and contralateral teeth was performed to determine the effect of possible microleakage on fractal dimension. METHODS: A total of 136 patients (170 teeth) identified in panoramic radiographs taken for diagnostic purposes between January 2018 and December 2023 at our Department of Oral and Maxillofacial Radiology were included in the study. Data were analysed using IBM SPSS V23. The Chi-square test was used for comparing categorical variables between groups. The relationship between the FD values calculated around the apexes of the teeth with unilateral dens invaginatus and the contralateral teeth was analyzed by paired t test. A significance level of p < 0.050 was adopted. RESULTS: The mean age of the cases was calculated as 28.1 (8-63) years. 66 (48.5%) of the cases were female, and 70 (51.1%) were male. The lateral incisor was the most affected tooth among these cases. Bilateral cases were observed in 34 patients. Type 2 was detected in 93 patients, Type 1 in 35 patients, and Type 3 dens invagination in 8 patients. Dens invaginatus cases were observed in 134 maxillary and 2 mandibular teeth. Periapical lesions were seen in 22 of these cases. CONCLUSIONS: Dens invaginatus cases are a congenital anomaly encountered at any age. Early diagnosis is crucial to prevent the loss of pulp vitality due to these invaginations. It should be noted that these invaginations can affect both jaws. However, due to the prevalence of occurrence in the maxillary anterior teeth and asymptomatic nonvitality, particular attention should be paid to evaluating this region.

Comparison of periapical radiography, panoramic radiography, and CBCT in the evaluation of trabecular bone structure using fractal analysis.

OBJECTIVES: The aim of this study is to compare imaging techniques to evaluate trabecular bone structure using Fractal Analysis (FA). METHODS: Fifteen sheep hemimandibles were used for this study. Digital images were obtained using periapical radiography, panoramic radiography, and cone-beam computed tomography (CBCT). CBCT imaging was performed in standard (STD) and high-resolution (HR) modes. FA was conducted using ImageJ 1.3 software with the box-counting method on the images. The fractal dimension (FD) values were analyzed by the statistical software Jamovi 1.6.23. Statistical significance was accepted as p < 0.05. RESULTS: The highest mean FD value was the FD on digital periapical radiographs (PaFD) (1.28 ± 0.04), and the lowest mean FD value was the FD on standard resolution cone-beam computed tomography images (STD-CBCTFD) (1.12 ± 0.10). Although there was no statistically significant difference between the PaFD and the FD on digital panoramic radiographs (PanFD) (p = 0.485), the PaFD was found to be significantly higher than STD-CBCTFD (p < 0.001), and the FD on high-resolution cone-beam computed tomography images (HR-CBCTFD) (p = 0.007). The PanFD was found to be significantly higher than the STD-CBCTFD (p = 0.004). CONCLUSION: According to our results, in the evaluation of trabecular bone structure using FA, periapical radiographs and panoramic radiographs have similar image quality for assessment of the FD. On the other hand, CBCT results did not correlate with results from any of the other techniques in this study.

Box-Counting Fractal Analysis: A Primer for the Clinician.

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain.

Morphology and Fractal-Based Classifications of Neurons and Microglia in Two and Three Dimensions.

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than do neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well-described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has substantially contributed to classifying functional categories, where, in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions, including hyper-ramification. This chapter provides a review of the intimate relationships between neurons and microglia, by introducing 2D and 3D fractal analysis methodology and its applications in neuron-microglia function in health and disease.

BP neural network-based analysis of the applicability of NMF in side-step cutting.

Background: Although the spatio-temporal structure of muscle activation in cutting have been studied extensively, including time-varying motor primitives and time-invariant motor modules under various conditions, the factorisation methods suitable for cutting are unclear, and the extent to which each factorisation method loses information about movement during dimensionality reduction is uncertain. Research question: To clarify the extent to which NMF, PCA and ICA retain information about movement when downscaling, and to explore the factorisation method suitable for cutting. Methods: The kinematic data during cutting was captured with a Vicon motion capture system, from which the kinematic features of the pelvic centre of mass were calculated. NMF, PCA and ICA were used to obtain muscle synergies based on sEMG of the cutting at different angles, respectively. A back propagation neural network was constructed using temporal component of synergy as input and the kinematics data of pelvic as output. Calculation of the Hurst index using fractal analysis based on the temporal component of muscle synergy. Results: The quality of sEMG reconstruction is significantly higher with ICA (P < 0.01) than with NMF and PCA for the cutting. The NMF reconstruction has a high degree of preservation of movement, whereas the ICA loses movement information about the most of the swing phase, and the PCA loses information related to the change of direction. Hurst index less than 0.5 for all three angles of cutting. Significance: NMF is suitable for extracting muscle synergies in all directions of cutting. Information related to movement may be lost when using PCA and ICA to extract the synergy of cutting. The high individual variability of muscle synergy in cutting may be responsible for the loss of movement information in muscle synergy.